Question

Quality control studies for Speedy Jet Computer Printers show the lifetime of the printer follows a normal distribution with mean = 4 years and standard deviation = 0.78 years. The company will replace any printer that fails during the guarantee period. How long should Speedy Jet printers be guaranteed if the company wishes to replace no more than 10% of the printers?

Answer 1

About 3 years Speedy Jet printers be guaranteed.

Explanation:

Given : Quality control studies for Speedy Jet Computer Printers show the lifetime of the printer follows a normal distribution with

mean
`\mu = 4` and standard deviation
`\sigma = 0.78`

If the company wishes to replace no more than 10% of the printers.

To find : How long should Speedy Jet printers be guaranteed ?

Solution :

Using Z- table,

Z value corresponding to 10% or 0.10 = -1.28.

Applying z-score formula,

`z=(x-\mu)/(\sigma)`

The value of x is given by,

`x=(z* \sigma)+\mu`

Substitute the values,

`x=(-1.28* 0.78)+4`

`x=-0.9984+4`

`x=3.0016`

So, approx 3 years.

Therefore, About 3 years Speedy Jet printers be guaranteed.